Nadia is 15 years older than Stephanie. For the last 3 years, Nadia and Stephanie have been going to the same school. Fifteen years ago, Nadia was 4 times older than Stephanie. How old is Nadia now?
Answer: We can use the given information to write down two equations that describe the ages of Nadia and Stephanie. Let Nadia's current age be $n$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $n = s + 15$ Fifteen years ago, Nadia was $n - 15$ years old, and Stephanie was $s - 15$ years old. The information in the second sentence can be expressed in the following equation: $n - 15 = 4(s - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $s$ and substitute it into our second equation. Solving our first equation for $s$ , we get: $s = n - 15$ . Substituting this into our second equation, we get the equation: $n - 15 = 4($ $(n - 15)$ $ -$ $ 15)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 15 = 4n - 120$ Solving for $n$ , we get: $3 n = 105$ $n = 35$.